Fig. 2.

Stability conditions in the steal/punish game (assuming $ϵ=0.05$, $r_{p:s},r_{c:s}>\frac{1}{38}$, and $r_{p:s}+r_{c:s}<38$). When $\theta$ is high, only the familiar $(F{S}_{ϵ},A{P}_{ϵ})$ is stable (blue-green region). When $\theta$ is low, only the inverted $(A{S}_{ϵ},F{P}_{ϵ})$ is stable (orange region). In the middle region, both are stable, and risk-dominance is determined by the boundary [$(F{S}_{ϵ},A{P}_{ϵ})$ to the right and $(A{S}_{ϵ},F{P}_{ϵ})$ to the left]. The evolution of rigid punishment depends on the relative vulnerability of flexible strategies in each role (see SI Text).